Question

in mrs wilsons geography class, the student who achieves the largest increase in their test score between any two consecutive weeks of term wins a prize.

	week 1	week 2	week 3	week 4	week 5
alex	92	89	62	54	59
petro	51	52	86	86	60
dominic	45	48	59	49	80
hayley	98	90	56	65	92

a) which student wins the prize?

the students suggest changing the system so that the prize winner is the student who achieves the largest increase in their test score across three consecutive weeks of term (for example, the difference between week 2 and week 4).

b) which student would win the prize using this system?

Explanation:

Step1: Calculate Sandra's consecutive increases

Week2-Week1: $93-95=-2$; Week3-Week2: $60-93=-33$; Week4-Week3: $77-60=17$; Week5-Week4: $63-77=-14$. Max: 17

Step2: Calculate Alex's consecutive increases

Week2-Week1: $89-92=-3$; Week3-Week2: $62-89=-27$; Week4-Week3: $54-62=-8$; Week5-Week4: $59-54=5$. Max:5

Step3: Calculate Petro's consecutive increases

Week2-Week1: $52-51=1$; Week3-Week2: $86-52=34$; Week4-Week3: $86-86=0$; Week5-Week4: $60-86=-26$. Max:34

Step4: Calculate Dominic's consecutive increases

Week2-Week1: $48-45=3$; Week3-Week2: $59-48=11$; Week4-Week3: $49-59=-10$; Week5-Week4: $80-49=31$. Max:31

Step5: Calculate Hayley's consecutive increases

Week2-Week1: $90-98=-8$; Week3-Week2: $56-90=-34$; Week4-Week3: $65-56=9$; Week5-Week4: $92-65=27$. Max:27

Step6: Find max 3-consecutive increase (a)

Sandra: $77-95=-18$, $63-93=-30$; Alex: $54-92=-38$, $59-89=-30$; Petro: $86-51=35$, $60-52=8$; Dominic: $49-45=4$, $80-48=32$; Hayley: $65-98=-33$, $92-90=2$. Max:35

Answer:

a) Petro
b) Petro